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The presence of dc offsets results in fundamental frequency oscillations in the frequency estimation and it is a challenging problem in single-phase grids. In this article, a four consecutive samples (4CSs) based method is proposed to estimate grid frequency with strong dc offset rejection capability. In details, a 4CS model is established based on the relationship among the fundamental grid voltage, dc offsets, and their consecutive sample signals. Different from the traditional 3CS model, the proposed 4CS model can reject the negative effects of dc offsets completely. Based on the obtained model, a frequency estimation is proposed and stability analysis is provided according to the adaptive control theory. Unlike the traditional 3CSs relying on prefilters, the proposed method is filter-free and it still has strong suppression capability against dc offsets. The theoretical sound and experimental results indicate that the proposed method achieves accurate frequency estimation with good dc offset rejection capability. [ABSTRACT FROM AUTHOR]